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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 logarithm/80371: I would like a solution to how it is done to evaluate each expression: log of 3 with the square root of 3. I do know the answer is 1/2 (from the back of my text book's answers to the problem), but the log calculator on this web site had the answer as 0 because it was needed 0 divisions to get to 1. Please explain . My question is written below ___ log _/3 31 solutions Answer 57662 by stanbon(57361)   on 2007-05-01 22:57:03 (Show Source): You can put this solution on YOUR website!log of 3 with the square root of 3. ------------ log(base 3) sqrt3 = 1/2 Why? log means exponent and 3^(1/2) = sqrt3 Notice that the exponent is 1/2; that's why the log is 1/2. ========== cheers, Stan H.
 Surface-area/80369: I would appreciate any help you can give me. A spherical water tank is 12.6 ft. in diameter. What is the weight of the water in the tank if water weighs 62.4 lb/ft cubed? Thank You, makennedy011 solutions Answer 57661 by stanbon(57361)   on 2007-05-01 22:48:51 (Show Source): You can put this solution on YOUR website!A spherical water tank is 12.6 ft. in diameter. What is the weight of the water in the tank if water weighs 62.4 lb/ft cubed? --------------- Volume = (4/3)(pi)(6.3)^3 Volume = 1047.39 cu ft Weight = (1047.39)*62.4 = 65357.41 lbs. ------------ Cheers, Stan H.
 Angles/80367: A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing? I'm new to the site so I'l work on making a picture. Thank you and it would be nice if youd show me the steps.1 solutions Answer 57659 by stanbon(57361)   on 2007-05-01 22:33:43 (Show Source): You can put this solution on YOUR website!The area of the circle the cow could cover if the barn was not there is (pi)50^2 But the barn cuts of 1/4th of the circle leaving 3/4 th of the circle for the cow to graze. Grazing area = (3/4)(pi)50^2 = 5890.49 sq ft ---------- Cheers, Stan H.
 Rational-functions/80362: Hi, I need help with this. Can anyone lend a hand? Here it is: If the expression: - 8w-5 over 6w+5 is to make sense, the values that w can take must be restricted. State the restriction on w. I'm not too sure how to type it but it looks something like this: 8w-5 - ---- 6w+5 Thank you so much for any help!!1 solutions Answer 57658 by stanbon(57361)   on 2007-05-01 22:29:07 (Show Source): You can put this solution on YOUR website!The denominator, 6w+5, must not be zero; when is that? 6w+5=0 when w=-5/6 So, w can be any Real Number except w= -5/6 ------------- Cheers, Stan H.
 logarithm/80364: I would like a solution to how it is done to evaluate each expression: log of 2 (log of 2, 4). I do know the answer is 1. Please explain . Thank you, Charles1 solutions Answer 57656 by stanbon(57361)   on 2007-05-01 22:22:25 (Show Source): You can put this solution on YOUR website!log means "exponent" log(base 2) 2 = 1 That means the exponent of "2" that results in the number 2 is 1. 2^1 = 2 Notice that "1" is the exponent, or log ======================== Cheers, Stan H.
 Travel_Word_Problems/80361: Tom walked to the meeting at 2 miles per hour and caught a ride home in an old truck at 10 miles per hour. How far was it to the meeting place if his total travel time was 18 hours?1 solutions Answer 57655 by stanbon(57361)   on 2007-05-01 22:18:26 (Show Source): You can put this solution on YOUR website!Tom walked to the meeting at 2 miles per hour and caught a ride home in an old truck at 10 miles per hour. How far was it to the meeting place if his total travel time was 18 hours? ---------------------- Let time at 2 mph be "x" ; distance walked = rt= 2x miles Time at 10 mph is "18-x" ; distace by truck = rt= 10(18-x)=180-10x miles --------------- distance walked = distance rode 2x=180-10x 12x=180 x=15 hrs Distance to the meeting place = 15 hrs*2mph = 30 mi ---------- Cheers, Stan H>
 Quadratic_Equations/80348: The sum of two numbers is 12. Their product is 36. Find the two numbers.1 solutions Answer 57652 by stanbon(57361)   on 2007-05-01 21:48:10 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 12. Their product is 36. Find the two numbers. ------------- Let one of the numbers be "x". Then the other number is "12-x". ------------ EQUATION: x(12-x)=36 12x-x^2 = 36 x^2-12x+36=0 (x-6)(x-6)=0 x=6 (one of the numbers) 12-6=6 (the other number) ================================ Cheers, Stan H.
 Radicals/80357: How do you solve or simlify √2+√6 / √8+√6 1 solutions Answer 57649 by stanbon(57361)   on 2007-05-01 21:32:10 (Show Source): You can put this solution on YOUR website!(√2+√6) / (√8+√6) Multiply numeratorand denominator by (sqrt8-sqrt6) to get: [(sqrt2+sqrt6)(sqrt8-sqrt6)]/[2] =[4-2sqrt3+4sqrt3-6]/2 =[-2+2sqrt3]/2 =[-1+sqrt3] ================== Cheers, Stan H.
 Circles/80354: Can anyone help me with this problem? Find the capacity, in gallons, of a cylindrical tank having a diameter of 8.00 ft. 8.00 in. and an altitude of 12.0 ft. Thank You, makennedy011 solutions Answer 57645 by stanbon(57361)   on 2007-05-01 21:25:21 (Show Source): You can put this solution on YOUR website!Find the capacity, in gallons, of a cylindrical tank having a diameter of 8.00 ft. 8.00 in. and an altitude of 12.0 ft. -------------------------- 8'8" = [8 2/3]' ----------------------- Volume = (pi)r^2h Volume = (pi)(26/3)^2(12)=901.333 cu. ft. ----------------------- Cheers, Stan H.
 Graphs/80353: If P(4, -5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6). 1 solutions Answer 57644 by stanbon(57361)   on 2007-05-01 21:13:54 (Show Source): You can put this solution on YOUR website!If P(4, -5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6). ========== The x-6 moves the point 6 units to the right, to (10,-5) The 2 doubles the y value so the final position is (10,-10) =========== Cheers, Stan H.
 Inequalities/80310: My question is from a work sheet. Two trains in opposite direction pass each other on parallel tracks. One train averages at most 80 km/h, and the other averages at most 65km/h. What is the least possible time that it could take for the two trains to be 290 km apart. TOTALLY LOST!!!1 solutions Answer 57615 by stanbon(57361)   on 2007-05-01 18:08:38 (Show Source): You can put this solution on YOUR website!Two trains in opposite direction pass each other on parallel tracks. One train averages at most 80 km/h, and the other averages at most 65km/h. What is the least possible time that it could take for the two trains to be 290 km apart. ---------- Let x be the time needed for them to be 290 km apart. 1st train goes =<80x km 2nd train goes =<65x km -------------- INEQUALITY: 80x+65x=<290 km 145x =< 290 km x =< 2 hrs x = 2 hrs =============== Cheers, Stan H.
 Inequalities/80308: Please help me with this story problem involving inequalities. Carlos has more than 80 coins, all nickels and dimes. He has five more dimes than nickels. What is the least mumber of nickels that Carlos can have? My work: n+d>80 d=n+5 n+n+5>80 2n>75 ?????1 solutions Answer 57613 by stanbon(57361)   on 2007-05-01 17:56:36 (Show Source): You can put this solution on YOUR website!Please help me with this story problem involving inequalities. Carlos has more than 80 coins, all nickels and dimes. He has five more dimes than nickels. What is the least mumber of nickels that Carlos can have? My work: n+d>80 d=n+5 n+n+5>80 2n>75 n>37 1/2 n >= 38 The least number of nickels is 38 ---------- Cheers, Stan H.
 Inequalities/80307: My question is off a worksheet that if called Solving problems involving inequalities. It is "Find the largest pair of consectutive integers whos sum is less than 85." My work is: x+x+2<85 2x<831 solutions Answer 57612 by stanbon(57361)   on 2007-05-01 17:43:44 (Show Source): You can put this solution on YOUR website!"Find the largest pair of consectutive integers whose sum is less than 85." ------ Let the consecutive integers be "x" and "x+1" EQUATION: x+x+1<85 2x < 84 x < 42 x=41 and x+1=42 ============ Cheers, Stan H.
 Equations/80306: simplify: (2+i)squared - (3+i)1 solutions Answer 57609 by stanbon(57361)   on 2007-05-01 17:35:46 (Show Source): You can put this solution on YOUR website!simplify: (2+i)squared - (3+i) ------------ 4+4i-1 -3-i =0 + 3i ============== Cheers, Stan H.
 Geometry_Word_Problems/80300: The circumference of a circle is 20Pi. What is the area of the circle? Leave your answer in terms of Pi1 solutions Answer 57606 by stanbon(57361)   on 2007-05-01 17:32:03 (Show Source): You can put this solution on YOUR website!The circumference of a circle is 20Pi. What is the area of the circle? Leave your answer in terms of Pi ----- Circmference = (pi)d = 20pi Therefore diameter = 20 and radius=10 ------------- Then Area = (pi)r^2 = (pi)10^2 = 100pi =============== Cheers, Stan H.
 Graphs/80278: what is the true equation for 2a+5b=3 is it (1/2, _4/5) or (0, 3/5). Can you show me how you came up with the answer1 solutions Answer 57596 by stanbon(57361)   on 2007-05-01 16:33:55 (Show Source): You can put this solution on YOUR website!what is the true equation for 2a+5b=3 is it (1/2, _4/5) or (0, 3/5). Can you show me how you came up with the answer ----------- To test (1/2, -4/5) substitute 1/2 in place of a and -4/5 in place of b and see if you get a true statement: 2(1/2) + 5(-4/5) = 3 1-4 = 3 -3=3 No, that is not true. ---------------------- To test (0,3/5) substitute 0 in place of a and 3/5 in place of b. 2*0 + 5*(3/5) = 3 0 + 3 = 3 3= 3 Yes, that is true. So (0,3/5) is the solution for the equation. ============= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/80267: can you help me find the correct answer. find the center and the radius of the circle x^2+y^2+6y-27=01 solutions Answer 57595 by stanbon(57361)   on 2007-05-01 16:27:33 (Show Source): You can put this solution on YOUR website!find the center and the radius of the circle x^2+y^2+6y-27=0 ------------- Complete the square on the x-terms and the y-terms respectively: --------- [x^2] + [y^2+6y + ?] = 27+? (x-0)^2 + (y^2+6y+(6/2)^2) = 27 + 9 (x-0)^2 + (y+3)^2 = 36 Center at (0,-3) Radius= 6 -------------- cheers, Stan H.
 Functions/80269: Given the function y=0.02x^2 + 1.9x - 5, complete the following table: x / y ___________ -125 / ? 100 / ? -75 / ? -50 / ? -25 / ? -0 / ? 25 / ?1 solutions Answer 57593 by stanbon(57361)   on 2007-05-01 16:20:38 (Show Source): You can put this solution on YOUR website!Given the function y=0.02x^2 + 1.9x - 5, complete the following table: Use your calculator to get: ---------------- x / y ___________ -125 / 70 100 / 385 -75 / -35 -50 / -50? -25 / -40? -0 / -5 25 / 55 ========== Cheers, Stan H.?
 Expressions-with-variables/80277: Please help I have been trying to figure this problem out but am unable to even get started -9x+2y=2 +6x+8y=-61 solutions Answer 57592 by stanbon(57361)   on 2007-05-01 16:15:46 (Show Source): You can put this solution on YOUR website!-9x+2y=2 +6x+8y=-6 ---------- Plan to get rid of the y terms so you can solve for "x". -------------- Multiply the 1st equation by 4 to get: -36x+8y=8 --------- Subtract that from the 2nd equation to get: 42x=-14 x=-1/3 ---------- Substitute that back into one of the earlier equations to solve for "y". 6x+8y=-6 6*(-1/3)+8y=-6 -2 + 8y = -6 8y = -4 y=-1/2 ----------- Solution x=-1/3 ; y=-1/2 ============== Cheers, Stan H.
 Expressions-with-variables/80275: Hello Could you please help me with this? M= 2x+y+2z/6 For x1 solutions Answer 57591 by stanbon(57361)   on 2007-05-01 16:10:48 (Show Source): You can put this solution on YOUR website!M= (2x+y+2z)/6 6M = 2x+y+2z 2x = 6M-y-2z x = 3M-(1/2y)-z =============== Cheers, Stan H.
 Graphs/80210: The line that has y intercept of 2 and x intercept of 51 solutions Answer 57590 by stanbon(57361)   on 2007-05-01 16:08:13 (Show Source): You can put this solution on YOUR website!The line that has y intercept of 2 and x intercept of 5 ---------- y-intercept: (0,2) x-intercept: (5,0) slope = 2/-5 = -2/5 y=mx+b y=(-2/5)x+2 ========= Cheers, Stan H.
 Numeric_Fractions/80274: 305+ a / 6=66 Thanks! I hope that slash line means divided by...that what I meant. Its been a long time since I've done algebra...so this is stumping me!1 solutions Answer 57588 by stanbon(57361)   on 2007-05-01 15:58:53 (Show Source): You can put this solution on YOUR website!305+ a / 6=66 --------- When you post you should use parentheses so we can tell exactly what you mean. -------- Meaning #1: (305+a)/6 66 Multiply both sides by 6 to get: 305+a = 396 a= 396-305= 91 ----------- Meaning # 2: 305 + (a/6) = 66 Multiply both sides by 6 to get: 6*305 + a = 6*66 a= 6*66 - 6*305 a = (66-305)*6 a=-1434 ---------- See the difference parentheses makes. --------- Cheers, Stan H.
 Expressions-with-variables/80276: Could I please get some help with this? 1/2(2x+2a)=1/3(21+3b) For x1 solutions Answer 57587 by stanbon(57361)   on 2007-05-01 15:53:34 (Show Source): You can put this solution on YOUR website!1/2(2x+2a)=1/3(21+3b) For x --------- x+a = 7+b x=7+b-a ========= Cheers, Stan H.
 logarithm/80249: Write in Logarithmic form (4/11)^-3=1331/641 solutions Answer 57586 by stanbon(57361)   on 2007-05-01 15:51:46 (Show Source): You can put this solution on YOUR website!Write in Logarithmic form (4/11)^-3=1331/64 ---------- Log means "exponent". --------- The exponent you have is -3 The base is (4/11) The result is 1331/64 ------ Rewrite as log(base 4/11) 1331/64 = -3 ========== Cheers, Stan H.
 Functions/80272: I would be so grateful if someone could help me out with this. Thanks so much! Give the values of x which must be excluded from the domain of the following function. f(x)= x+1 ------- x^2-4x-12 I really appreciate any help on this!!!1 solutions Answer 57584 by stanbon(57361)   on 2007-05-01 15:41:38 (Show Source): You can put this solution on YOUR website!Give the values of x which must be excluded from the domain of the following function. f(x)= (x+1)/(x^2-4x-12) Factor to get: f(x)/[(x-6)(x+2)] ------------------ X-values are excluded if they make the denominator zero or if they make a radicand negative for radicals with even index. -------------- Your Problem: You have no radicals, so forget that. You have a denominator so x cannot be 6 and it cannot be -2. ------------ Therefore the domain is All Real Numbers except x=-2 and x=6. =========== Cheers, Stan H.
 Expressions-with-variables/80270: What is L=1/4r For r ?1 solutions Answer 57583 by stanbon(57361)   on 2007-05-01 15:37:21 (Show Source): You can put this solution on YOUR website!What is L=1/4r For r ? It means you should solve the equation for "r". L=(1/4)r Multiply both sides by 4 to get: 4L=r r=4L ============= Cheers, Stan H.
 Rational-functions/80246: i would really be thank u if u could help me out with this. thank so much Identify the horizontal asymptotes. f(x)=x-1/x-3 x=3 y=3 x=1 y=1 none Question 2 Identify the vertical asymptotes. f(x)=x-1/x-3 x=3 y=3 x=1 y=1 none Question 3 Identify the horizontal asymptotes. f(x)=x^2+1/x-2 x=1 y=1 x=2 y=2 none Question 4 Identify the vertical asymptotes. f(x)=x^2+1/x-2 x=1 y=1 x=2 y=2 none Question 5 2 points In the equation: y=3x x and y vary directly. True False Question 6 Save In the equation: xy=0.1 x and y vary directly. True False Question 7 In the equation: y=2/x x and y vary directly. True False Question 8 If z varies jointly with the product of x and y, find the constant of variation, k, given x=1/2, y=8, z=12. Enter only the numerical value of k. Question 9 Using the information in question #8, "If z varies jointly with the product of x and y, find the constant of variation, k, given x=1/2, y=8, z=12." Write an equation that relates the variables. Do not put any spaces between the numbers or variables in your equation. 1 solutions Answer 57581 by stanbon(57361)   on 2007-05-01 15:29:06 (Show Source): You can put this solution on YOUR website!Identify the horizontal asymptotes. f(x)=x-1/x-3 As x gets larger and larger f(x) gets closes and closer to x/x=1 x=1 is the horizontal asymptote. ----------- Question 2 Identify the vertical asymptotes. f(x)=x-1/x-3 Vertical asymptote when the denominator is zero: x=3 is a vertical asymptote. --------------- Question 3 Identify the horizontal asymptotes. f(x)=x^2+1/x-2 As x get larger of larger f(x) gets closer and closer to x^2/x=x which is infinity. So, no horizontal asymptote. ------------- Question 4 Identify the vertical asymptotes. f(x)=x^2+1/x-2 Denominator is zero when x=2; x=2 is the vertical asymptote. ------------ Question 5 2 points In the equation: y=3x x and y vary directly. True Because as x gets larger y gets larger; try it and you will see. ------------------- Question 6 Save In the equation: xy=0.1 x and y vary directly. False They vary indirectly; as x gets larger, y gets smaller so their product will stay the same; try it. ---------------- Question 7 In the equation: y=2/x x and y vary directly. False --------------- Question 8 If z varies jointly with the product of x and y: z=k(xy) find the constant of variation, k, given x=1/2, y=8, z=12: 12 = k(1/2*8); k=3 ------------------ Question 9 Using the information in question #8, "If z varies jointly with the product of x and y, find the constant of variation, k, given x=1/2, y=8, z=12." k=3 ================= Cheers, Stan H.
 Graphs/80258: Rewrite in standard form: (0,5),m=-3/5 Give your result in slope intercept form where possible I do not have a clue as to where to start with this problem, Please help!!1 solutions Answer 57579 by stanbon(57361)   on 2007-05-01 15:11:21 (Show Source): You can put this solution on YOUR website!Rewrite in standard form: (0,5),m=-3/5 Give your result in slope intercept form where possible ------------ You are given the slope and the y-intercept, so y=(-3/5)x+5 is the slope-intercept form of the line. ------------- To get the standard form, multiply thru by 5 to get: 5y=-3x+25 Rearrange to get the standard form which is ax+by=c 3x+5y=25 =========== Cheers, Stan H.
 Miscellaneous_Word_Problems/80224: If someone could show me how to get started - I would so greatful! Here is the whole problem: In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges \$2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each \$.25 increase in fare. Part One: Graph function,identify the graph of the function (line,parabola, hyperbola, exponential), find the slope of the graph, find the price at which there will be no more riders,a nd find the maximum number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the fare. (I have never been could with word problems - I just need help getting started) Part Two: The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is \$0 (free), how many riders are permitted each day? ( Must to first part to do this part) Part Three: If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus? ( Must do the rest in order to do this part)1 solutions Answer 57570 by stanbon(57361)   on 2007-05-01 11:12:27 (Show Source): You can put this solution on YOUR website!In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges \$2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each \$.25 increase in fare. Function is Income = (# of riders)(price paid): Let x = # of days Income = (1000-50x)(2.00+0.25x) I(x) = -(25/2)x^2+150x+2000 Part One: Graph function --------------- identify the graph of the function (parabola), --------------- find the slope of the graph: slope = -25x-150 ---------- find the price at which there will be no more riders: No riders means 1000-50x=0 50x=10000 implies x=20 Price when x=20 is \$2 + 20*0.25=\$7 --------- find the maximum number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the fare. You need a set of points of the form (2+0.25x,1000-50x): such as (2,1000), (1.75.25,1050),(1.50,1100)...(0,1400) -------------- Part Two: The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is \$0 (free), how many riders are permitted each day? Answered already above---#=1400 ------------------- Part Three: If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus? (2,1000), (2.25,950), (2.50,900)....(2+20*0.25,1000-20*50)=(7,0) No one will ride the bus when the price is \$7 =============== Cheers, Stan H.
 Equations/80226: Please help? These always confuse me. Simplify. x+2/x/x-2/3x These are the ones that look like fractions on top of fractions.1 solutions Answer 57564 by stanbon(57361)   on 2007-05-01 10:38:41 (Show Source): You can put this solution on YOUR website!Simplify. x+2/x/x-2/3x ------- Just remember: "invert the denominator and follow the rules of multiplication". --------- Your Problem: [(x+2)/x] / [(x-2)/3x] =[(x+2)/x] * [3x/(x-2)] Cancel the common factor of "x" to get: =[3(x+2)/(x-2)] ========= cheers, Stan H.
 Trigonometry-basics/80220: If csc theta=-5/4 and theta is in quadrant 3,then cos theta=1 solutions Answer 57561 by stanbon(57361)   on 2007-05-01 10:10:15 (Show Source): You can put this solution on YOUR website!If csc theta=-5/4 and theta is in quadrant 3,then cos theta=? --------- Draw the picture of theta in the 3rd quadrant. csc(theta)=r/y The terminal side passes thru the point (x,-4) and r=5. Find x where x^2+y^2=r^2 x^2=5^2-4^2=9 x=-3 in the 3rd Quadrant Therefore cos(theta)= x/r=-3/5 ========== Cheers, Stan H.